Title: Relational Latent Class Models

Volker Tresp (2)

With: Zhao Xu (1,2), Stefan Reckow (1,2), Achim Rettinger (2,4)
Kai Yu (3), Shipeng Yu (2) and Hans-Peter Kriegel (1)

(1) University of Munich, Germany, (2) Siemens AG, (3) NEC
Laboratories America (4) Technical University of Munich

Learning in relational domains is finding increasing interest. In
relational domains information about relationships is often more
informative than entity attributes. Thus known attributes are often
weak predictors for relationships. One way to think of this is to
assume that there are indeed strong entity attributes but
unfortunately they are unknown. This motivates the use of latent
variables in relational domains. Examples of latent class models are
the IHRM model (2006) and the DERL model from our group (2005), the
IRM model from Kemp et al. (2004, 2005), the MMSB models from Airoldi
at al. (2006), and the stochastic blockstructures (e.g., Nowicki and
Snijder, 2001). In my presentation I will focus on the IHRM/IRM models
and only briefly touch on the other approaches.

Infinite hidden relational models (IHRMs) apply nonparametric mixture
modeling to relational data. An IHRM introduces for each entity an
infinite-dimensional latent variable as part of a Dirichlet process
(DP) mixture model, which leads to three advantages. First, IHRM
reduces the extensive structural learning, which is particularly
difficult in relational models due to the huge number of potential
parents. Second, the information propagates globally in the ground
network defined by the relationship structure. Third, the number of
mixture components for each entity class can be optimized by IHRM
itself based on the data. The IHRM can be applied to entity
clustering, relation (link) prediction and attribute prediction. For
inference, we studied various approaches: Gibbs sampling with the
Chinese restaurant process, Gibbs sampling with truncated stick
breaking, and Gibbs sampling with Dirichlet-multinomial allocation, as
well as two mean-field approximations.

The performance of IHRM has been applied in several domains for movie
recommendations, for modeling gene interactions, for medical decision
support and for trust learning in multi-agent settings.